Structure and Infrastructure Engineering
Maintenance, Management, Life-Cycle Design and Performance
ISSN: 1573-2479 (Print) 1744-8980 (Online) Journal homepage: https://www.tandfonline.com/loi/nsie20
Risk-based inspection planning optimisation of
offshore wind turbines
José G. Rangel-Ramírez & John D. Sørensen
To cite this article: José G. Rangel-Ramírez & John D. Sørensen (2012) Risk-based inspection
planning optimisation of offshore wind turbines, Structure and Infrastructure Engineering, 8:5,
473-481, DOI: 10.1080/15732479.2010.539064
To link to this article: https://doi.org/10.1080/15732479.2010.539064
Published online: 04 Jan 2011.
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Structure and Infrastructure Engineering
Vol. 8, No. 5, May 2012, 473–481
Risk-based inspection planning optimisation of offshore wind turbines
José G. Rangel-Ramı́reza* and John D. Sørensena,b
a
Department of Civil Engineering, Aalborg University, Sohngaardsholmsvej 57, DK-9000 Aalborg, Denmark; bRisø DTU,
Frederiksborgvej 399, DK-4000 Roskilde, Denmark
(Received 15 May 2009; final version received 16 November 2009; accepted 4 November 2010; published online 4 January 2011)
Wind industry is substantially propelled and the future scenarios designate offshore locations as important sites for
energy production. With this development, offshore wind farms represent a feasible option to accomplish the needed
energy, bringing with it technical and economical challenges. Inspection and maintenance (I&M) costs for offshore
sites are much larger than for onshore ones, making the choice of suitable I&M planning for minimising costs
important. Risk-based inspection planning (RBI) for offshore installations represents a suitable methodology to
identify the optimal maintenance and inspection strategies to ‘control’ the deterioration in facilities such as offshore
wind turbines (OWT), where fatigue and corrosion are typically affecting these structures. This article considers an
RBI approach applied to OWT based on the developed methodologies for oil and gas installations, but considering
the lower reliability level for wind turbines. This framework is addressing fatigue prone details in welded steel joints
typically located in the wind turbine substructure. The increase of turbulence in-wind farms (IWF) due to wake
effects is taken into account using a code-based turbulence model. As part of the results, life cycle reliabilities and
inspection times are calculated for IWF location and single/alone location of OWT. The results indicate earlier
inspection times for IWF.
Keywords: inspection; reliability; decision analysis; fatigue; wake turbulence
1.
Introduction
Planned scenarios for wind energy in Europe expect
increasing need of installations for wind energy
production. According to European Wind Energy
Association (EWEA) the wind energy targets might
supply up to 20% of the European Union electricity
demand in 2020. The offshore production is expected
to contribute with up to 40%. Economical and
technical challenges are a consequence of the offshore
locations, which have advantages such as assuring the
transnational energy supply with an encourage of
interconnection of energy markets reducing the fuel
imports and generation of CO2 and deploying regional
development of coastal areas where maritime jobs are
in decline.
To accomplish the energy production targets,
clusters of offshore wind turbines (OWT) (wind farms)
are built, implying additional technical challenges
concerning the spatial interaction of OWT at downwind stream (wake effects) that affect the life-cycle
performance when the increase of loading and
turbulence decrease the OWT fatigue life.
At offshore sites, sea depth will impact the decision
whether a specific type of support structure will be the
optimal or not. The monopile foundation is typically
used for ‘shallow’ water depths while tripod and jacket
*Corresponding author. Email: jr@civil.aau.dk
ISSN 1573-2479 print/ISSN 1744-8980 online
Ó 2012 Taylor & Francis
http://dx.doi.org/10.1080/15732479.2010.539064
http://www.tandfonline.com
type foundation represent a suitable option at deeper
places. At very deep water (470 m) floating wind
turbines have to be used.
Operation and maintenance costs for OWT are
much larger than for onshore structures, making any
optimisation of inspection, operation and maintenance
planning very important to minimise the overall cost of
energy (COE).
Risk-based inspection (RBI) planning, understood
as an application of Bayesian decision analysis, has
been extensively applied in the oil and gas (O&G)
industry, see e.g. Faber et al. (2000), Sørensen and
Faber (2001) and Moan (2005). The aim is to the
identify the optimal inspection and maintenance
strategy using a suitable ‘control’ of deterioration at
important areas in the structure, taking into account
economical and technical aspects related with the
overall performance. In the O&G industry this
approach of I&M planning has been applied to fixed
steel offshore structures and then adapted to other
structures such as tankers, Floating, Production,
Storage and Off-loading facilities (FPSO’s), semisub’s, see e.g. Goyet et al. (2002) and at the latest to
onshore structures with deterioration mechanisms such
as corrosion and fatigue (e.g. reinforced concrete and
steel bridges). Unlike other structures with significant
474
J.G. Rangel-Ramı´rez and J.D. Sørensen
consequences of failure, OWT allows the use of costbenefit analyses due to their low risks to human lives,
society and environment.
Site conditions such as deep water, waves and
turbulence in-wind farms (IWF), affect detrimentally
the life-cycle performance of OWT. At deeper water
locations, jacket and tripod support structures stand
for more appropriate engineering solutions due to their
economical and technical improvements compared to
monopile support structures, e.g. due to reduced costs
concerning the amount of material, improved dynamical behaviour, structural redundancy, less impact area
for extreme wave and scour conditions. However, for
IWF locations of wind turbines, the turbulence coming
from the surrounding OWTs will affect considerably
the inner or down-wind turbines due to wake effects
decreasing the fatigue life and thus the reliability level.
In this article is considered how to apply RBI planning
optimisation for fatigue prone welded details in jacket
and tripod types of OWT steel support structures. The
fatigue failure limit state is the primary limit state to be
considered for welded steel connections in e.g. transition nodes and tower in tripod and jacket support
structures. In many cases the design-driver for these
structural parts is the fatigue performance. Details
made of cast steel are not considered in this article, but
the same techniques can be expected also to apply here.
Probabilistic models and representative limit state
equations for ultimate structural fatigue failure are
formulated and illustrative examples are described,
considering fatigue failure using both linear and
bilinear SN-curves and for single and IWF locations.
2.
Wind load and wind farm turbulence
The land wind variation is higher than for offshore
sites, which are typically characterised by higher wind
speeds and lower turbulence. In near shore locations,
the influence of the coastal line affects the wind flow
boundary layer that grows through the proximal
20 km off the coastline. This change is principally
related to the difference of surface roughness, where
sea roughness is typically much smaller than the land
one.
This difference between stability conditions on- and
off-shore is affecting the wind speed profile and
additionally IWF’s turbulence and other wake effects
will play an important role in terms of wind energy
production and fatigue, see Figure 1. It is seen that the
turbulence level increase up to 50% and the mean wind
speed decrease up to 10% within a wind farm.
For OWT in water depths up to approximately 25
m, wind load is typically dominating the wave load,
partly due to the influence of the active control of the
wind turbine for power output. For wind turbines in
Figure 1. Ratio swf/s0 between standard deviation of
turbulence in wake within wind farm and outside wind
farm and ratio Uh/U between mean wind speed within wind
farm and outside wind farm – both as function of mean
wind speed U. The solid lines are model prediction. From
Frandsen (2005).
operation, the passive, active or mixed power control
assure a rational and stable output of electricity and
protect structural and electromechanical parts from
overload. It is noted that fatigue contributions from
events such as start and stop of the wind turbine and
accidental shut-downs are not included in the models
of this article.
Depending on the wind direction a wind turbine
within a wind farm will be exposed to free wind or
wake conditions. In Frandsen (2005) is defined an
equivalent standard deviation of the turbulence behind
a wind turbine taking into account the possibility of
wake turbulence:
m 1=m
se ¼ ð1 NW pW Þsm
ð1Þ
u þ NW pW sW
where su is the turbulence standard deviation under
free flow condition (equal to s0 in Figure 1). sW is the
maximum standard deviation of turbulence under
wake condition, pW( ¼ 0.06) is the probability of a
wake condition, m is the Wöhler exponent in a relevant
SN-curve and NW is the number of neighbouring wind
turbines to which the considered wind turbine is
exposed. In this model, it is assumed that the standard
deviation of the response is proportional to the
standard deviation of turbulence. In certain situations
(e.g. using passive or active power control; in complex
terrain and atypical terrain conditions) this simple
relation with the response may be inadequate, see
Figure 2.
The above mentioned turbulence model seems to be
consistent (with a slightly conservative inaccuracy of
Structure and Infrastructure Engineering
3–4%) when it is used with superimposed deterministic
load components, see Sørensen et al. (2007).
3. Inspection and maintenance planning
The overall goal for inspection and maintenance
strategies are to minimise the overall service life costs
while a minimum reliability level should be achieved.
This decision process can be carried out into a
framework of pre-posterior analysis from classical
decision theory, see Raiffa and Schlaifer (1961),
Benjamin and Cornell (1970) and Ang and Tang
(1975). Due to the random nature of degradation
processes at offshore sites, a probabilistic approach is a
rational tool to deal with a highly uncertain deterioration process since probabilistic and statistical models
can be formulated that includes the uncertainties
Figure 2. Standard deviation of wind speed measured at
hub height and standard deviation of flapwise blade bending
moment as function of the wind direction. The bending
moment and the wind speed are scaled to ambient conditions
at wind directions 260–3608. Data are from Vindeby Wind
Farm. Figure is from Frandsen (2005).
Figure 3.
RBI decision process
475
coming from external agents and conditions (e.g.
wind, wave conditions, soil conditions etc), model
uncertainties, human-actions (e.g. design, inspection,
maintenance and repair, etc) and internal processes
(e.g. degradation).
During the last two decades, risk-based approaches
for inspection and planning have been developed, see
Skjong (1985), Madsen et al. (1987), Thoft-Christensen
and Sørensen (1987) and Fujita et al. (1989), aiming at
the identification of suitable I&M planning strategies,
satisfying reliability requirements and minimising the
life cycle overall costs.
The decision process can be summarised as
described in the following and illustrated in Figure 3.
At the first stage the structure is conceived at the initial
design phase where the dimensions and materials are
defined according to optimal design parameters z ¼ (z1,
z2, . . . ,zN), taking into account code and practical
requirements. The installed structure will be affected
by external agents, e.g. wind, wave and corrosion
modelled by random states of nature X0. If the
statistical basis for evaluation of the uncertainties is
limited then also model and statistical uncertainties
will become important.
Monitoring activities ‘e’ at the times t ¼ (t1,
t2, . . . , tn), include inspection and monitoring actions
which result in inspection results ‘S ’ (degree of wear
and corrosion, denting level, size of fatigue cracks . . .)
that are obtained depending on inspection quality
q ¼ (q1, q2, . . . ,qn), (inspection techniques, technical
expertise of inspectors, etc.). Based on these monitoring results, mitigation alternatives will be considered
regarding a fixed or adapting mitigation policy
modelled by a decision rule d(S). Such policies are
related to repair, replacement or doing nothing
activities based on the degree of damage. When these
476
J.G. Rangel-Ramı´rez and J.D. Sørensen
mitigation actions have been done a state of nature Xi
will be the beginning of new random outcomes due to
the external exposure and damage process in the time
interval to the next inspection. These posterior states of
nature depend on assumptions established to simplify
the RBI decision process, e.g. assuming that repaired
components behave like new component and repaired
parts will have no indication at the inspection.
In Figure 3, CT(z,e,S,d(S),X) are the total service
life costs where X ¼ (X0, X1,X2, . . .). The optimal
design and decision parameters (z,e,d(S))) in the
inspection and maintenance strategy are determined
form the following optimisation problem where the
expected value of CT(z,e,S,d(S),X) is minimised:
min E½CT ðz; e; S; dðSÞ; XÞ
¼ CI ðzÞ þ E CInsp ðz; e; S; dðSÞ; XÞ
þ E CRep ðz; e; S; dðSÞ; XÞ þ E½CF ðz; e; S; dðSÞ; XÞ
s:t: zmin
xi zmax
i
i
DPF;t ðt; z; e; dÞ DFmax
F
i ¼ 1; 2; . . . ; N
t ¼ 1; 2; . . . ; TL
ð2Þ
where TL is the service life, CI is the initial costs, E[CInsp]
is the expected inspection costs, E[CRep] is the expected
repair costs and E[CF] is the expected failure costs.
Equation (2) is constrained by limits on design
parameters and that the annual probability of failure
DPF,t has to be less than DFmax
F . The n inspections
are performed at times ti, i ¼ 1, 2, . . . , n where
t0 t1 t2 tn TL.
Total capitalised expected inspection costs are:
E CInsp ðz; e; S; dðSÞ; XÞ
n
X
CInsp;i ðqÞð1 PF ðti ÞÞ
¼
i¼1
1
ð1 þ rÞti
ð3Þ
where the index i characterises the capitalised inspection costs at the ith inspection when failure has not
occurred earlier, CInsp,i(q) is the inspection cost of the
ith inspection, PF(ti) is the probability of failure in the
time interval [0,ti] and r is the real rate of interest, i.e.
the inflation is not included.
Total capitalised expected maintenance and repair
costs are:
n
X
E CRep ðz; e; S; dðSÞ; XÞ ¼
CRep;i ðqÞPRep;i ðti Þ
i¼1
1
ð1 þ rÞti
ð4Þ
where index i characterise the capitalised repair costs at
the ith inspection when failure has not occurred earlier,
CRep,i(q) is the cost of maintenance and repair
(including loss of production) at the ith inspection
and PRep,i(ti) is the probability of performing a repair
after the ith inspection when failure has not occurred
earlier. Estimation of PRep,i(ti) is explained in Sørensen
and Faber (2001).
The total capitalised expected costs due to failure
are:
E½CF ðz; e; S; dðSÞ; XÞ ¼
TL
X
CF ðtÞDPF;t PCOLjFAT
t¼1
1
ð1 þ rÞti
ð5Þ
where index t represents time, CF(t) is the cost of
failure (incl. loss of production), DPF,t is the annual
probability of failure and PCOLjFAT is the conditional
probability of collapse of the structures given fatigue
failure of the considered component.
Since a posterior Bayesian statistical basis is used
inspection and monitoring data can be used to update
the RBI plans making the process a recursive activity,
see Sørensen et al. (1991). This updating can be used
for structural and mechanical parts (tower, blades,
support structures, wind energy converter components) of the wind turbine.
4.
Probabilistic modelling of fatigue failure
The probabilistic models for assessing the fatigue failure
life based on SN-curves and fracture mechanics (FM)
model are briefly described in the following. For RBI
planning, the FM model is usually calibrated such that
the same reliability level is obtained as using a codebased SN model. The probabilistic model to evaluate
the fatigue life is based on Sørensen et al. (2007) and the
wake model described in detail by Frandsen (2005). For
this model, the number of surrounding wind turbine is
limited to eight wind turbines while the arrangement of
the wind turbines is typically chosen to produce as little
mutual wake effects as possible.
For the free flow ambient turbulence conditions
and for the assessment of the SN-fatigue life, a deterministic design equation is formulated which uses the
equivalent fatigue stress range concept. Fatigue accumulation in the operational mode is considered for a
specific design life TL and a typical number of fatigue
load cycles per year. The design equation is written:
n FDF TL
GðzÞ ¼ 1 KC
Z Uout ^ u ðU Þ
s
D m; aDs ðUÞ
fU ðUÞdU ¼ 0 ð6Þ
z
Uin
^u ðUÞ is the characteristic value of the
where s
standard deviation of the turbulence su(U) at mean
477
Structure and Infrastructure Engineering
wind speed U. su(U) is modelled as a Lognormal
distributed stochastic variable with mean value equal
to Iref (0.75 U þ b) and standard deviation equal
to 1.4m/s Iref. Iref is the IEC 61400–1 (2005)
reference turbulence intensity (equal to 0.14 for
medium turbulence characteristics). The characteristic
^u ðUÞ is defined as the 90%
ambient turbulence s
quantile value.
The standard deviation of stress ranges sDs as
function of the mean wind speed U is assumed to be
modelled by, see Equation (6)
sDs ðUÞ ¼ aDs ðUÞ su ðUÞ
z
accumulation, t is the life time in years, XW is the
model uncertainty related to wind load effects (exposure, assessment of lift and drag coefficients,
dynamic response calculation), XSCF is the model
uncertainty related to local stress analysis.
For an IWF location the design equation is given
by:
n FDF TL
KC
2
s
^ u ð UÞ
Z Uout ð1 NW pW Þ D m; aDs ðUÞ z
6
6
Nw
P
4
^ ðUÞ
s
Uin
þpW D m; aDs ðUÞ u;jz
GðzÞ ¼ 1 ð7Þ
3
7
7
5
j¼1
Here aDs(U) is an influence coefficient function and z is
a design parameter (e.g. proportional a cross sectional
area).
For a linear SN-curve the damage function D in (6)
is modelled by:
Z 1
DL ðm; sDs ðUÞÞ ¼
sm fDs ðsjsDs ðUÞÞds
ð8Þ
fU ðUÞdU
ð11Þ
^u;j ðUÞ is the standard deviation of turbulence from
s
neighbouring wind turbine no. j:
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
u
u
0:9 U2
^2u
^u;j ðUÞ ¼ t
ð12Þ
s
pffiffiffiffiffiffiffiffiffi 2 þ s
1:5 þ 0:3 dj U=c
0
and for a bi-linear SN-curve:
Z
DsD
DBL ðm1 ; m2 ; DsD ; sDs ðUÞÞ ¼
Z0
sm1 fDs ðsjsDs ðUÞÞds
where dj is the distance to neighbouring wind turbine
no j normalised by the rotor diameter and c is a
constant equal to 1 m/s.
The limit state equation corresponding to the
above design equation is:
1
þ
sm2 fDs ðsjsDs ðUÞÞds:
gðtÞ ¼ D DsD
ð9Þ
In Equation (6) n is the total number of fatigue load
cycles per year, FDF is the fatigue design factor
(FDF ¼ TF/TL)), TF is the fatigue design life, KC is
the characteristic value (defined by mean log K
minus two standard deviation of log K) of K
(material parameter), Uin and Uout are the cut-in
and -out wind speed, respectively, fU(U) is the
density function of mean wind speed U fDs(SjsDs(U)) is the density function for stress ranges
given standard deviation sDs at mean wind speed U.
This density function and n can be obtained by
counting methods, e.g. Rainflow counting.
The time-dependent limit state equation corresponding to Equation (6) is:
Z
Z
n t Uout 1
gð t Þ ¼ D ðXW XSCF Þm
K Uin
0
su ðUÞ
D m; aDs ðUÞ
fsu ðsu jUÞ fU ðUÞdsu dU
z
ð10Þ
where D is a stochastic variable modelling the
uncertainty related to the Miner rule for damage
nt
K
Z
Uout
Uin
Z
1
ðXW XSCF Þm
0
ð1 NW pW Þ D m; aDs ðUÞ su ðzUÞ
6
6
Nw
P
4
s ð UÞ
þpW D m; aDs ðUÞ u;jz
2
3
7
7
5
j¼1
fsu ðsu jUÞ fU ðUÞdsu dU
ð13Þ
where
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
u
u
Xwake U2
su;j ðUÞ ¼ t
pffiffiffiffiffiffiffiffiffi 2 þ s2u
1:5 þ 0:3 dj U=c
ð14Þ
Xwake is the model uncertainty related with total/
equivalent wake turbulence model and XW is the
uncertainty related to the model in Equation (12) for
increased turbulence in a wake. The design parameter z is calculated with Equation (6) or (11) and
then used in limit state Equation (10) or (13) to
estimate the reliability index or the probability of
failure at time t.
For the assessment of the FM-fatigue life a onedimensional crack model is used, see Figure 4. The
crack length c is assumed to be related to the crack
478
J.G. Rangel-Ramı´rez and J.D. Sørensen
depth a through a factor fcr. It is assumed that the
fatigue life may be represented by a fatigue initiation
life and a fatigue propagation life:
N ¼ NI þ NP
ð15Þ
where N is the number of stress cycles to fatigue
failure, NI is the number of stress cycles to crack
propagation and NP is the number of stress cycles from
initiation to crack through. The correlation between NI
and NP is taken into account by a correlation coefficient r, see Lassen (1997). The crack growth can be
described by the following equations:
da
¼ CA ðDKA Þm ;
dN
aðNI Þ ¼ ao
c ¼ fcr a
ð18Þ
CA and m are the material parameters, ao describes the
initial crack depth after NI cycles. DKA is the stress
intensity range.
The stress range Dsis obtained from:
ð19Þ
where Y is the model uncertainty variable related to
geometry function and Dse is the equivalent stress
range. For a single OWT Dse is obtained from:
Uin
1
Dðm;sDs ðUÞÞ
0
1=m
fsu ðsu jUÞfU ðUÞdsu ðUÞdU
77
77
57
7
5
:
ð21Þ
The limit state criteria used in the FM analysis is
defined as the event that the crack exceeds a critical
crack size:
ð22Þ
ð16Þ
ð17Þ
Ds ¼ Y Dse
3 31=m
fsu ðsu jUÞ fU ðUÞdsu dU
gðtÞ ¼ ac aðtÞ
pffiffiffiffiffiffi
DKA ¼ Ds ap
Dse ¼XW XSCF
Z Uout Z
Dse ¼ XW XSCF 2
2
su ð U Þ
Z Uout Z 1 ð1 NW pW Þ D m; aDs ðUÞ z
6
6
6
6
Nw
P
4
6 U
s ðUÞ
0
þpW D m; aDs ðUÞ u;jz
6 in
4
j¼1
ð20Þ
where ac is the critical crack size and a(t) is crack
depth.
The incorporation of inspection’s uncertainty (inspection methods, technology, environmental conditions, inspectors’ expertise, etc) will be through a
distribution of the detectable crack size or probability
of detection curve (POD) such as the following:
PODðxÞ ¼ P0 ð1 exp ðx=lÞÞ
ð23Þ
where l is a parameter describing the expected length
of defects detected and P0 is a parameter modelling the
probability of detecting very large defects.
5.
Examples
A steel jacket support structure of an OWT is
considered. The OWT is assumed to have an expected
lifetime equal to 20 years ( ¼ TL) and design fatigue life
times equal to 40, 50 and 60 years ( ¼ TF). An influence
coefficient function aDs(U) representing the mudline
bending moment is shown in Figure 5. It is representative for a fatigue critical detail in the support
structure and/or the transition node at the mudline
and for an IWF location:
Figure 4.
loads.
Surface crack idealisation in plate under fatigue
Figure 5. aDs(U)/su(U) for mudline bending moment –
pitch controlled wind turbine.
479
Structure and Infrastructure Engineering
for a pitch controlled wind turbine. The aDs(U)
function is highly non-linear due to the control system.
Linear (L) and Bilinear (BL) SN-curves are considered
for an IWF location (IWF) and a single/stand alone
wind turbine (S). For the stochastic model two cases
will be considered with two levels of uncertainties.
Tables 1 and 2 show the two stochastic models (case A
and B) and the distribution parameters.
The design value z for each case is shown in Table 3
determined from Equations (6) and (11). In Figures 6
and 7 are shown the reliability index bt as function of
time t for the stochastic model case A with TF ¼ 50
years and using the SN approach (limit state equations
in Equations (10) and (13)).
The results in Table 1 show that the design values
for cases IWF are larger than the ones for free flow
Table 1.
Variable
D
Xw
XSCF
Xwake
ln CA
NI
Y
DsD
log K1
log K2
TF
NW
n
Uin7Uout
PiW
di
aC
ao
fcr
Thickness
m
turbulence. This is due to the additional accumulation
of fatigue from wake turbulence. Further, it is seen
that the design values using a bilinear SN-curve are
smaller than using a linear SN-curve.
The results in Figures 6 and 7 show that the
reliability level is slightly lower for wind turbines
within a wind farm compared to ‘stand-alone’ wind
turbines – although they are designed using design
equations (Equation (11)) that takes into account the
wake effects. For all cases, a FM model is calibrated
using the reliability indices in the interval from 10 to 20
years, see Figure 7.
In Figure 7 is shown the reliability as function of
time obtained with SN- and FM-approaches where the
FM model is calibrated to the same reliability level as
the code-based SN model. The annual probability of
SN- and FM-stochastic models.
Distribution
Expected value
N
LN
LN
LN
N
W
LN
D
N
N
D
D
D
D
D
D
D
D
D
D
D
1.0
1.0
1.0
1.0
mln CA (fitted)
mNI ¼ Tinit n
1.0
71 MPa
Determined from DsD
Determined from DsD
40, 50 and 60 years
5/–
56107
5–25 m/s
0.06/–
4.0
50 mm
0.4 mm
4.0
50 mm
3.0
Standard deviation
0.10 (A)/0.15
0.10 (A)/0.05
0.10 (A)/0.05
0.15 (A)/0.10
0.77
0:35 mNI
0.10
–
0.20
0.25
–
–
–
–
–
–
–
–
–
–
–
(B)
(B)
(B)
(B)
Comment
Damage accumulation
Wind
Stress concentration factor
Wake
Crack growth rate
Tinit (fitted), Initiation time
Shape factor
Constant amplitude fatigue limit
Material parameter
Material parameter
Fatigue life
In-wind farm/single OWT
Fatigue cycles per year
Cut-in – cut-out wind velocities
In-wind farm/single OWT
Normalised distance of OWT
Critical crack size
Initial crack size
Crack length/depth ratio
thickness
Material parameter
Note: log K1 and log K2 are assumed fully correlated and ln CA and NI are correlated with correlation coefficient¼70.5.
(A) first case and (B) second case.
D, Deterministic; N, Normal; LN, LogNormal; W, Weibull.
Table 2.
Distribution parameters and equations.
Variable
Distribution
Parameters
Comment
DPF
fU(U)
fDsD()
fsu()
POD(x)
N1(s)
N2(s)
D
W(a,bU)
W(aDsD,bDsD)
LN(m,s)
Equation (24)
K1s7m1
K2s7m2
161073/161074
a ¼ 2.3, bU ¼ 10.0 m/s
aDsD ¼ 0.8
m ¼ Iref(0.75Uþ3.8), s ¼ 1.4 m/sIref.
PO ¼ 1.0, l ¼ 2.67 mm
s DsD
s 5 DsD
Annual maximum probability of failure
Mean wind speed
Stress ranges
Mean turbulence
Probability of detection
SN curve linear
SN curve bi-linear
D, Deterministic; N, Normal; LN, LogNormal; W, Weibull.
480
Table 3.
J.G. Rangel-Ramı´rez and J.D. Sørensen
Design parameters z.
TF
IWF–L
S–L
IWF–BL
S–BL
40
50
60
0.4939
0.5321
0.5654
0.4309
0.4642
0.4934
0.3841
0.4049
0.4253
0.3306
0.3482
0.3657
Table 4. Inspection times are shown obtained solving the risk
based optimisation problem with the fatigue reliability
probabilistic model, using a maximum acceptable annual
probability of failure DFFmax ¼ 1:0 104 .
Inspection times (year)
TF
Case
(A)
(B)
40
IWF – L
S–L
IWF – BL
S – BL
IWF – L
S–L
IWF – BL
S – BL
IWF – L
S–L
IWF – BL
S – BL
9
17
6
8
12
–
9
11
18
–
11
15
16
–
14
18
–
–
–
–
–
–
–
–
50
60
Figure 6. Reliability index for SN-approach corresponding
to the cumulative probability of failure of case A with
TF ¼ 50 years.
first inspection time, slightly earlier inspections are
obtained for IWF location due to the increase of
fatigue coming from the increased wake turbulence.
For case B, the first inspections will come
(significantly) later due to lower uncertainty level for
this case. Further, higher fatigue lifetimes, TF imply
that the first inspection comes later. It is noted that for
all the cases the design parameter z is determined by a
deterministic design such that the code-based design
criteria is exactly satisfied.
6.
Figure 7. Reliability indices for SN- and calibrated FMapproach corresponding to the cumulative probability of
failure of case A with TF ¼ 40 years.
failure DPF,t is obtained as DPF,t ¼ PF(t)7PF(t71)
where PF(t) ¼ F(7bt).
In Table 4, inspection times are shown obtained
solving the risk based optimisation problem with the
fatique reliability probabilistic model, using a maximum acceptable annual probability of failure DF equal
to 1.0 1074. It is noted that the results are obtained for
a case where the reliability constraint in Equation (2) is
active and the costs are not relevant. Comparing the
Conclusion
A model for optimal inspection and maintenance
planning is presented based on the same principles as
used for offshore oil and gas installations. It is applied
for fatigue failure limit states for welded steel details in
jacket support structures for OWT. Both wind turbines
within a wind farm and wind turbines not influenced of
other wind turbines are considered using a probabilistic model for fatigue failure. Wake effects are taken
into account for wind farms.
This RBI-approach used for inspection planning
for OWTs represents a rational and practical tool to
optimise I&M activities, assuring that a minimum
reliability level is satisfied. This article considers
components in wind turbine support structures (structural components) that in case of failure will trigger
major consequences for the whole wind turbine. The
same method could also be used for other components
in wind turbines such as blades, main frame and cast
components.
For wind farms with many wind turbines, a
rational planning of inspection and maintenance
activities should consider the whole wind farm as a
Structure and Infrastructure Engineering
system and include correlation between failure modes
and inspection results in different wind turbines. This
can be done using the same principles as described in
this article. Furthermore, it could also be applied as a
decision tool for estimating the consequences of
possible service life extensions. For very large offshore
wind farms where construction and installation will
take many months or years, the wind turbines during
this process will be exposed to different conditions, first
they will be exposed as a single wind turbine and later
to wake turbulence conditions within the wind farm.
Modifications to the methodology can be done to take
into account these different stages during the life-cycle
of an OWT.
Acknowledgements
The financial support from the Mexican National Council of
Science and Technology (CONACYT) and the project
‘Probabilistic design of wind turbines’ supported by the
Danish Research Agency, grant no. 2104–05–0075 is greatly
appreciated.
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